In this paper, Lattice-Discrete Particle Model (LDPM) of concrete has been extended in 2-D to account for the effect of non-circular aggregates. To this end, the flexible equation of super-ellipse is employed for generating aggregates in order to add the simulation possibility of a greater spectrum of aggregate samples in 2-D to lattice-Discrete particle Model. Alongside this extention, required procedures for the generation of aggregates, their packing in space, the determination of influencing region of each particle, the definition of interacting surfaces and computational points and the definition of strains are outlined. Finally, the effects of aggregates geometry on macro-scale compressive strength and softening curve and also cracking pattern of concrete under uniaxial compression are discussed.